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The University of Massachusetts basketball team had not played at TD Garden in more than a decade, its program deemed not quite worthy of the big stage in Boston. Second-year coach Derek Kellogg changed that, arranging for last night’s game against Memphis.

The Minutemen are sure to be invited back.

Freshman Terrell Vinson picked up a loose ball in the lane and scored with less than a second left as UMass came away with a stunning 73-72 victory before a crowd of 8,096.

Wearing throwback jerseys from the 1970s, UMass built a 7-point lead in the second half, lost it, then showed the poise to get it back just in time.

“This game means a lot to us,’’ Kellogg said. “We need to let people in this area know that the state school has a good team they can support. I’m thrilled, I really am.’’

Memphis (7-2) took a 72-69 lead on a jumper by Wesley Witherspoon with 3:07 left. But the Tigers could not put the Minutemen away, missing their next three shots. Two free throws by Ricky Harris with 47 seconds left cut into the Memphis lead.

Memphis called time with 31 seconds remaining and ran a play for Elliot Williams, a talented Duke transfer. But he missed, giving UMass a shot.

The Minutemen tried to get the ball inside, but it was tied up with 3.8 seconds left. The Minutemen retained possession and Kellogg drew up a play intending to get a lob to guard Anthony Gurley. But the play went awry and the ball bounced off several hands to Vinson, who was standing just inside the foul line.

“I never expected I would get it,’’ said Vinson, whose 21 points were a career best. “The clock was running out and I knew I had to shoot it.’’

The officials reset the clock to 0.7 seconds after Vinson’s shot. Witherspoon missed a heave at the buzzer.

It was an emotional victory for Kellogg, who spent eight seasons at Memphis as an assistant under former coach John Calipari before returning to his alma mater in 2008. Kellogg pumped his fist to the crowd as he left the court.

“I know those kids personally. I know their families. Memphis as a city and a school still holds a place for me,’’ said Kellogg, who helped recruit nearly every player on the Memphis roster. “I would have probably have preferred that both of us could have come away with a win. But I’m glad we won.’’

The Minutemen matched their season high with 20 turnovers and missed 12 of their 32 free throws. But a 44-24 rebounding advantage led to 21 second-chance points and erased those mistakes. The Minutemen scored 40 of their points in the paint.

“I think rebounding is one of the most important things in the game,’’ Kellogg said. “If you can dominate the boards, it gives you extra opportunities.’’

Memphis fell, 57-55, against No. 1 Kansas Nov. 17, missing a shot at the buzzer. The Tigers won their next six games by an average of 25.3 points, taking advantage of a soft nonconference schedule. Only one of those games was on the road and the Tigers arrived in Boston primed to be upset.

“We are small, that’s an issue. We have to take the pain from this game and learn from it,’’ Memphis coach Josh Pastner said. “I saw the ball bouncing around at the end and I thought we were going to win it. But they made a play. They deserved to win.’’

The Minutemen will be back in Boston on Wednesday, playing Boston College at Conte Forum. They will return with a dose of confidence.

“This game means a lot. People in the Boston area usually don’t get to see UMass too often,’’ said Gurley, a junior guard who starred at Newton North High School. “It was a good showcase for us. It lets people know there’s stuff going on in Western Mass.’’